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Curriculum Vitae

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Email: dylan.costa@uconn.edu

Last updated: October 25, 2026

Research Interests

Algebraic Number Theory and Arithmetic Geometry, with a focus on elliptic curves, modular curves, and Galois representations attached to abelian varieties.

Education

University of ConnecticutPhD in Mathematics | Advisor: Álvaro Lozano-Robledo
2021 – 2027 (expected)
Ithaca CollegeBA in Mathematics, with Honors | Advisors: Emilie Wiesner & Ted Galanthay
2017 – 2021

Teaching Experience

Instructor of Record

MATH 2410: Elementary Differential Equations2 sections of 40 students each semester
Fall 2025, Spring 2026
MATH 1071: Calculus for Business and Economics2 sections of 40 students each semester
Fall 2023, Spring 2024, Spring 2025

Graduate Teaching Assistant

MATH 1131: Calculus I2 sections of 40 students each semester
Fall 2026, Fall 2021
MATH 3160: Probability (Online)
Summer 2025, Summer 2026
MATH 2110: Multivariable Calculus3 sections of 40 students each semester
Summer 2024, Fall 2024
MATH 1132: Calculus II3 sections of 40 students each semester
Spring 2022, Summer 2022, Fall 2022, Spring 2023, Summer 2023, Summer 2026

Mentoring

Independent Study: CryptographyUniversity of Connecticut
Spring 2026 – Present
Directed Reading Project in Algebraic Number TheoryUniversity of Connecticut | Directed Reading Program
Fall 2025
Directed Reading Project on Algebraic CurvesUniversity of Connecticut | Directed Reading Program
Spring 2024

Publications

ℓ-primary Torsion in Elliptic Curves over ℚWith Álvaro Lozano-Robledo and Enrique González-Jiménez.
In preparation
Classification of Isogeny-Torsion Graphs in Quadratic FieldsWith Rakvi.
In preparation
Elliptic Curve Rank Growth in Multi-Quadratic ExtensionsWith Álvaro Lozano-Robledo. Preprint: arXiv:2610.31925
Preprint, October 2026
An Elliptic Curve of Rank ≥ 34 and Root Number −1 over a Quadratic FieldWith Álvaro Lozano-Robledo. Preprint: hexagon:2610.00280
Preprint, October 2026

Invited Talks

Recent Discoveries on Ranks of Elliptic CurvesSIGMA Graduate Seminar, University of Connecticut
October 2026
A Computational Perspective on Modular CurvesNumber Theory Reading Group, University of Connecticut
November 2025
Rank Growth of Elliptic Curves over Quadratic ExtensionsSIGMA Graduate Seminar, University of Connecticut
August 2025
Elliptic Curves and their Applications in Mathematics and BeyondMathematics Colloquium, Ithaca College
April 2025
Pontryagin Duality and Applications to Tate's ThesisNumber Theory Reading Group, University of Connecticut
March 2025
Rank Growth of Elliptic Curves over Quadratic ExtensionsGraduate Research Forum, University of Connecticut
January 2025
On ℓ-adic Images of Galois Attached to Elliptic Curves over the RationalsGeneral Exam Presentation, University of Connecticut
November 2024
On the Euclidean Embedding and Adeles/Ideles of a Number FieldNumber Theory Reading Group, University of Connecticut
October 2024
Construction of High Rank Elliptic Curves over Quadratic FieldsNumber Theory Reading Group, University of Connecticut
April 2024
Elliptic Curves and their ApplicationsMathematics Continued Conference, University of Connecticut
March 2024
On Meromorphic Differentials and Riemann-RochNumber Theory Reading Group, University of Connecticut
April 2023

Awards

Summer Travel FellowshipUniversity of Connecticut
Summer 2026
Oracle Honors SocietyIthaca College
Fall 2019 – Spring 2021
Summer Scholar FellowshipIthaca College
Summer 2020
Ramanujan Award in MathematicsIthaca College
Fall 2019

Relevant Skills

Programming: MAGMA, SAGE, Java (advanced), Python, MATLAB (intermediate), HTML (novice)
Software: LaTeX, Excel, Google Sheets